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Decomposable Robust Two-Stage Optimization: An Application to Gas Network Operations Under Uncertainty

  • We study gas network problems with compressors and control valves under uncertainty that can be formulated as two-stage robust optimization problems. Uncertain data are present in the physical parameters of the pipes as well as in the overall demand. We show how to exploit the special decomposable structure of the problem in order to reformulate the two-stage robust problem as a standard single-stage optimization problem. Since this structure is present in similar problems on e.g., water or direct current electricity networks, we investigate the consequences of the decomposable structure in an abstract setting: The right-hand side of the single-stage problem can be precomputed by solving a series of optimization problems and multiple elements of the right-hand side can be combined into one optimization task. In order to apply our results to gas network problems, we extend piecewise relaxations and preprocessing techniques to incorporate uncertain input data. The practical feasibility and effectiveness of our approach is demonstrated with benchmarks on realistic gas network instances. We observe large speedups due to the described aggregation method together with the developed preprocessing strategies. Furthermore, we are able to solve even comparably large gas network instances quickly for the price of slightly more conservative solutions.

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Metadaten
Author:Denis Aßmann, Frauke Liers, Michael Stingl
Document Type:Preprint
Language:English
Date of Publication (online):2017/11/20
Date of first Publication:2017/11/20
Release Date:2017/11/20
Tag:gas networks; relaxations; robust optimization
Institutes:Friedrich-Alexander-Universität Erlangen-Nürnberg
Subprojects:B06